If chess was a war then positional play, or strategy, would be the big picture objectives:
- capture this bridge
- move the front forward
- bring back private Ryan

Tactics would be the execution and local skirmishes:
- call in an airstrike because we are pinned down by artillery
- distract that sniper while I go around behind him
- use sticky bombs on those tanks

Without good tactics, you'll lose every fight. Without good positional play/strategy, you'll get into the wrong fights or bad fights. Good positional play helps you get better skirmishes, because your forces are better in number or location.

When a player is playing tactically, they think "if he does this, then I do this, then he does this..." If a winning tactic exists, a player can use a forcing series of a moves to gain an advantage.

When a player is playing positionally, they are considering long term strategic ideas. Answering questions like, "how can I improve my bishop?", or "how can I weaken his pawn structure?" or "how do I increase my grip on the dark squares?"

As /u/HDRgument said, successful chess requires both aspects of thinking. You may need to analyze tactical sequences to ensure your positional plan is possible.

All chess is tactical. When two very good players play, they usually cannot force an advantage through tactics because they can both see the tactical patterns well enough that neither will fall victim to the tactics that present themselves in a relatively even position. So, they use clever moves, and often tactical threats, to create smaller, positional advantages. Eventually, these advantages will build on each other, and one side will have much more active pieces than the other, and an unstoppable winning combination will present itself. This combination may either be directly tactical (an outright checkmate or win of material), or simply a sequence of exchanges that creates a winning endgame.

Positional chess includes tactical chess. Often, a beginner has a line of thinking like "I am not very good at tactics, so I will become a positional player!" This is putting the cart before the horse, and sets them up for failure. In reality, in order to play positional chess, you must first be very good at tactics.

Like I said in another thread, there is nothing more embarassing than playing a beautiful positional squeeze for 30 moves and then losing a knight to a pawn fork. Believe me, I've been there.

Positional play may be defined as play directed at neither attacking nor defending, but instead improving the overall quality of a player's position through the application of general principles of positional theory, as opposed to detailed analysis of a particular position. Tactical play, on the other hand, is directed at obtaining an advantage through the application of tactical motifs which are present in a particular position.

The description of general principles as strategy and particular positions as tactics feels a little off to me. In a particular position your opponent might have a weak square which you can fight for control over using strategy/general principles.